A unit fraction contains 1 in the numerator. The decimal representation of the unit fractions with denominators 2 to 10 are given:
1/2 = 0.5
1/3 = 0.(3)
1/4 = 0.25
1/5 = 0.2
1/6 = 0.1(6)
1/7 = 0.(142857)
1/8 = 0.125
1/9 = 0.(1)
1/10 = 0.1
Where 0.1(6) means 0.166666..., and has a 1-digit recurring cycle. It can be seen that 1/7 has a 6-digit recurring cycle.
Find the value of d < 1000 for which 1/d contains the longest recurring cycle in its decimal fraction part.
In [1]:
open System.Collections.Generic
let rec maxPatternLength' num den pos (remainders:IDictionary<int,int>) =
let rem = num % den
if remainders.ContainsKey(rem) then
pos - remainders.[rem]
else
remainders.Add(rem, pos)
maxPatternLength' (10 * rem) den (1 + pos) remainders
let maxPatternLength n =
maxPatternLength' 1 n 0 (new Dictionary<int, int>())
[2..1000]
|> List.map (fun n -> (n, (maxPatternLength n)))
|> List.sortBy (fun (n, patternLength) -> patternLength)
|> List.last
|> fst
|> printfn "%A"
In [ ]: